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Re: Partial Differential Equation


Philippe,

The problem you have posed is a 2-point boundary value problem which Mathematica 
often has difficulty with. The solution is to turn it into a one-point BVP, 
and find the initial condition on T(0) that gives the desired T'(1). The 
technique is often called a shooting technique.

I have sent you a NB separately that gives my attempt.

Cheers,

Kevin

The wise words of P. Poinas on 13 Jan 2001 22:47:38 -0500:

> Dear Group,
> 
> I am trying to solve the following problem:
> 
> \!\(\(\(NDSolve[{\(T''\)[R] + \((1/\((R + 0.05)\))\)\ \(T'\)[R] -
>           10\^\(-8\)\ \ T[R]\^4 == 0, \(T'\)[0] == \(-0.07\), \
> \(T'\)[1] ==
>         0}, \ T, \ {R, \ 0, \ 1}]\)\(\ \)\)\)
> 
> and I get the following message:
> 
> NDSolve::"inrhs": "Differential equation does not evaluate to a number
> or the \
> equation is not an nth order linear ordinary differential equation."
> 
> I know that this error is because I am defining the derivative at 2
> different R values:
> 
> at R=0, T'[0 ]= -0.07
> and R=1, T'[1] = 0
> 
> hence it is not an initial boundary condition.
> 
> 1) How can I turn around the problem?
> 
> 
> Actually, I found the Mathematica Book (V4) very weak on the subject. In
> page 924, it seems possible in In[7] to find a solution to a linear
> differential equation, even with 2 boundary conditions defined at 2
> different x values! My problem being not linear cannot therefore be
> solved. But Mathematica does not mentioned the linearity as a show
> stopper.
> 
> 2) Does anybody know a better description of Mathematica's capacity?
> 
>         Thank you for helping me,
> 
> 
>                         Philippe Poinas
> 
> 



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